The method emerges directly from the method for reconstruction of a three-dimensional image volume described in DE 10 2006 041 033.5 published after the filing date of the present application. Whereas with conventional methods for determining gray-scale values for volume elements of bodies to be mapped at predetermined rotational positions of the x-ray image recording system a 2D x-ray image (projection image) is recorded in each case, DE 10 2006 041 033.5 deals with the problem that this projection image is not sufficient to fully map a body to be mapped. Instead, only parts of the body are mapped in a projection image. In DE 10 2006 041 033.5 the problem is solved in that at least two different projection images of such a body to be mapped are recorded in each case for the predetermined rotational positions of the x-ray image recording system. The projection images are not recorded randomly, but a constant relative position between the focal point of the x-ray source and the area of interest of the body to be mapped is common to the at least two different projection images, a triangle being formed for this purpose between the focal point and two points in the area of interest, said triangle being displaced by rotations about the focal point, in order to distinguish one of the different projection images from the other. The at least two different projection images are not directly back-projected in the method for reconstruction of a three-dimensional image volume. Instead, a virtual projection image is created, in which in contrast to the individual different real projection images the body to be mapped is actually displayed in full. To create the common virtual projection image, a predefined mapping rule is used. The virtual projection image is now used to calculate, using back projection onto the volume elements, contributions to the gray-scale values assigned to the rotational position, one contribution to each rotational position in each case. The contributions to all rotational positions are then summed to form the gray-scale values to be determined.
If as in this case back-projection is used, calibration is required. For example, when an x-ray C-arm is rotated, vibrations occur when the system is accelerated. The projection parameters for each recording position should now be determined under recording conditions during calibration. The projection parameters are normally summarized in a projection matrix. The projection parameters are used to described the projection geometry. For each point in the projection image it is determined which view ray determines the gray-scale value at this point, i.e. how the line appears from the focus of the x-ray source to the x-ray detector.
In connection with the method of filtered back-projection, the use of a “calibration phantom” is known, which is shown in FIG. 1 and designated there as a whole by 10. A calibration phantom is a body known by predetermined individual features. The mapping conditions, i.e. the projection parameters, are inferred from the mappings of the individual features. Details of the calibration phantom shown in FIG. 1 are described in the article by N. Strobel, B. Heigl, T. Brunner, O. Schütz, M. Mitschke, K. Wiesent, T. Mertelmeier: “Improving 3D Image Quality of X-Ray C-Arm Imaging Systems by Using Properly Designed Pose Determination Systems for Calibrating the Projection Geometry” from Medical Imaging 2003: Physics of Medical Imaging; edited by Yaffe, Martin J.; Antonuk, Larry E. in Proceedings of the SPIE, Vol. 5030, pp. 943-954, 2003.
The calibration phantom 10 consists of a plastic cylinder 12 transparent to x-rays, in which 108 balls 14 are embedded. The balls are made of non-corroding steel and thus act as markers in the x-ray images. The balls are arranged helically. The helical arrangement of the markers has the advantage that especially in the case of circular scanning tracks, as are normal with x-ray C-arms, sinusoidal curves can be identified in the projection images, i.e. as many markers as possible are optimally mapped simultaneously. The balls 14 of the calibration phantom can be of two different sizes: the small balls have a diameter of 1.6 mm, and the large balls a diameter of 3.2 mm. The choice of large and small balls for a particular location in the helix is effected by way of coding, producing binary coding thanks to the opportunity to provide two different sizes of ball. The coding is selected so that a partial sequence of eight balls is sufficient in the mapping if their different sizes can be identified in the projection image, to assign precisely which eight balls from the 108 balls have been mapped in the projection image. The calibration phantom 10 is used to determine the projection parameters for a (filtered) back-projection, the following steps being performed:
1.) Locating the 2D marker position in the projection image,
2.) Determining the sequence of the 2D marker position (along the helix), especially using a sinusoidal mapping of the helix,
3.) Assigning the 2D marker position to the 3D marker locations in the helix using the coding,
4.) Determining the projection matrix for each scanning point using the 2D-3D marker correspondences.
The problem of performing a calibration during the method for reconstruction of a three-dimensional image volume known from DE 10 2006 041 033.5 rests on the fact that although projection images are likewise recorded there, they are not themselves used for back-projection, but are initially mapped to a (common) virtual projection image, the virtual projection image only then being back-projected.